When recording income for a marketplace startup, is it typical to use the gross transaction or just the fees collected per payment?

You usually only recognize the commissions as revenues and use the term "Gross Merchandise Value" (GMV) to describe the size of the marketplace (value of all transactions going through the site)

You would include all those lines in your revenue.

Typically this looks like:

Receipts: [full cash inflows]
Fees: [payouts to vendors]
Gross Receipts: [subtract]

This ALL does into the Revenue category, so that your stated revenue is indeed net of fees, but you can see how it breaks out to understand how money is moving.

That's if the margin there is very slim. If the margin is pretty good, and if you believe you can increase that margin materially over time, you can consider putting those fees into your gross margin instead of in your income.

From a P&L standpoint, if the revenue comes through your accounts at all, it's good to have a gross revenue line because you'll be carrying a cash balance on your balance sheet from these transactions before you reconcile with the marketplace that would appear high. Every organization is different but consider looking up showing Gross Revenue and then Net Revenue in your income section. Net Revenue is not to be confused with Net Income.

I believe that GMV concept will be helpful in solving your problem. Gross Merchandise Value, also referred to as gross merchandise volume, is the total amount of sales a company makes over a specified period, typically measured quarterly or yearly. While Gross Merchandise Value can be useful for a company in terms of understanding how many items are being sold and the amount of revenue being generated from them, it ultimately provides unrefined data that does not really express the true value of the goods being sold or business profitability.
You can read here: https://corporatefinanceinstitute.com/resources/knowledge/finance/gross-merchandise-value-gmv/
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Depending on the type of marketplace site, GMV is not the same as gross revenue. Example for sites like eBay, it is a reflection of the total value of goods sold, but not the actual revenue the company makes, as a portion of those revenues is for the sellers of the goods.

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